The phase plane method for the solution of equations applied to semiconductor device modelling

Abstract

AbstractA new method is introduced for solving the sets of discretized non‐linear equations which arise in the modelling of semiconductor microwave devices. The technique involves writing the functions to be solved as the right‐hand sides of damped differential equations. Following the solution path of these equations in phase space leads to the equilibrium point which corresponds to the solution of the original set of equations. An error analysis is made of the method, and the method is illustrated by applying it to a model of a four‐layer HEMT with two recesses and a fieldplate. In the early stages of developing the modelling equations for a new device, it is necessary to be able to add or subtract features into the equations; the main benefit of the method introduced here is that the minimum amount of preparation needs to be done in order to discretize the amended equations. Copyright © 2004 John Wiley & Sons, Ltd.